let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated halting AMI-Struct of N
for F being Instruction-Sequence of S
for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let S be non empty IC-Ins-separated halting AMI-Struct of N; :: thesis: for F being Instruction-Sequence of S
for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let F be Instruction-Sequence of S; :: thesis: for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let s be State of S; :: thesis: for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let k be Element of NAT ; :: thesis: ( F . (IC (Comput (F,s,k))) = halt S implies Result (F,s) = Comput (F,s,k) )
assume A1: F . (IC (Comput (F,s,k))) = halt S ; :: thesis: Result (F,s) = Comput (F,s,k)
then A2: F halts_on s by Th31;
dom F = NAT by PARTFUN1:def 2;
then CurInstr (F,(Comput (F,s,k))) = halt S by A1, PARTFUN1:def 6;
hence Result (F,s) = Comput (F,s,k) by A2, Def8; :: thesis: verum